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Calculate the value of gamma for a gaseo...

Calculate the value of `gamma` for a gaseous mixture consisting of `n_(1)` moles of oxygen and `n_(2)` moles of carbon of carbon dioxide. The values of `gamma` for oxygen and carbon dioxide are `gamma_(1) and gamma_(2)` respectively. Assume the gases to be ideal.
[Hint: `U_(m) = U_(1) + U_(2) and U = (nRT)/(gamma-1)`]

Text Solution

Verified by Experts

`U_(m) = U_(1) + U_(2)`
`U_(1) = (n_(1)RT)/(r_(1) - 1) U_(2) = (n_(2)RT)/(r_(2)) - 1`
`U_(m) = (n_(1) +n_(2)RT)/(r_(mix) - 1)`
`(n_(1) + n_(2)RT)/(r_(mix) - 1) = (n_(1)RT)/(r_(1) -1) + (n_(2)RT)/(r_(2) - 1)`
`(n_(1) + n_(2))/(r_(mix) - 1) = (n_(1)(r_(2) - 1))/(r_(1)-1) + (n_(2)(r_(1)-1)/(r_(2)-1)`
`(n_(1)+n_(2))(r_(1)-1)(r_(2)-1)/(n_(1)(r_(2)-1) + (n_(2)r_(2)-1) + r_(mix)`
`r_(mix) = (r_(1)r_(2)n_(1) +n_(2)) -n_(1)r_(1) +n_(2)r_(2))/(n_(1)r_(2)-1)+n_(2)r_(2)-1)`
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Calculate the value of gamma for a gaseous mixture consisting n_(1) moles of oxygen and n_(2) moles of carbon dioxide. The values of gamma for oxygen and carbon dioxide are gamma_(1) and gamma_(2) respectively. Assume the gases to be ideal.

Calculate gamma of a gaseous mixture consisting of 3 moles of nitrogen and 2 moles of carbon dioxide.

Knowledge Check

  • The value of gamma=C_p/C_v for a gaseous mixture consisting of 2.0 moles of oxygen and 3.0 moles of helium. The gases are assumed to be ideal.

    A
    `7/5`
    B
    `29/19`
    C
    `23/19`
    D
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  • A mixture of n_1 moles of monoatomic gas and n_2 moles of diatomic gas has gamma=1.5

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    `n_1=n_2`
    B
    `2n_1=n_2`
    C
    `n_1=2n_2`
    D
    `n_1=3n_2`

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